The "Operating Limitations" will require an annual "Program Letter" to
be sent to the local FSDO/FAA and placed in your aircraft folder.

I have seen this. I have also seen Operating Limitations that do not
specify that Program Letters be submitted.

I have looked for a FAR or AC that requires Program Letters (in
general) to be submitted for Experimental Aircraft. So far I haven't
found any such regulation.

-Pat